This is an old posting, so probably you have already found more about your ancestry.
But just in case you didn't and are still monitoring this site, the descending generations are as follows:
William Nathan Adkinson b. 1750-52 VA d. 26 Feb 1838 and wife Sarah Lee b. Abt. 1756 NC d. Duplin-Sampson County, NC Robert Adkinson b. 1779 (prob. NC) d. 26 Jan 1877 Coffee County, AL and wife Ann Lowe George Washington Adkinson and wife Rebecca Mancil William Green Adkinson & wife